revenue, profit, maximum, maximum profit. Please help.

Question

A charter bus has determined thatt the cost, in dollars, of providing x people a tour is C(x)=180+2.50x. A full tour consists of 78 people. The ticket price per person is $17 plus $0.25 for each unsold ticket.

(a) Determine the revenue function.

 

(b) Determine the profit function.

 

(c) Determine the company's maximum profit.

 

(d) Determine the number of ticket sales that yields the maximum profit.

Answer 1

a. Revenue _max = sold tickets * ticket price, the maximum, in this case, would be 78 * $17 = $1,326 

 

b. Profit _max = Revenue _max - Cost  = $1,326 - [$180 + ($2.50 * 78)] - ($0.25 * unsold)

        if the number of unsold tickets = 0, then Profit _max    = $1,326 - $180 - $195 = $951

 

c. the maximum Profit will be earned if all the tickets are sold.

 

Given the information in this problem, the breakeven point would occur when 12 tickets are sold

recovering the fixed cost of $180  means $180/17 = 11 tickets; the variable cost ($0.25 for each unsold ticket) multiplied by 67 (78 tickets - 11 to break even) = $16.75, which is approximately one ticket. Thus, 12 tickets to breakeven.